Meta-abelian unit groups of group algebras are usually abelian

DOI10.1016/0022-4049(91)90067-CzbMath0735.16020MaRDI QIDQ1176697

Aner Shalev

Publication date: 25 June 1992

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

group algebrasfinite groupsAbelian groupsunit groupsmetabelian groups

Mathematics Subject Classification ID

Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Units, groups of units (associative rings and algebras) (16U60)

Related Items (12)

On the derived length of the unit group of group algebras of groups with cyclic commutator subgroup ⋮ A NOTE ON THE DERIVED LENGTH OF THE UNIT GROUP OF A MODULAR GROUP ALGEBRA ⋮ On group algebras with metabelian unit groups ⋮ Modular group algebras with centrally metabelian unit groups ⋮ Group rings with solvable unit groups of minimal derived length. ⋮ ON THE DERIVED LENGTH OF THE GROUP OF UNITS OF A GROUP ALGEBRA ⋮ GROUP ALGEBRAS WITH UNIT GROUPS OF DERIVED LENGTH THREE ⋮ On the derived length of the unit group of a group algebra ⋮ On group algebras whose group of units has maximal derived length ⋮ Group rings with metabelian unit groups ⋮ Mod \(2\) group algebras with metabelian unit groups ⋮ Engel properties of group algebras. II

Cites Work

• The center of crossed products over simple rings
• Über den Frobenius'schen Klassenbegriff in nilpotenten Gruppen
• Observations on group rings
• On the Solvability of Unit Groups of Group Algebras
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